This subsection provides more detail on how we use an inverse graphics model, DECA [1]}, to control the pose of faces generated by StyleGAN2 trained on FFHQ 1024\(^2\) , as introduced in Section REF .
Recall that we use the conditional INN extension, detailed in Algorithm REF , for this experiment.
To enable generating different poses of the same identity, we add additional identity energy using the IR-SE50 model [2]}.
The training algorithm is detailed in Algorithm REF .
Specifically, we generate a canonical latent code \(\mathbf {z}_0 = f_{\mathbf {\theta }}(\mathbf {\epsilon }, \mathbf {\rho }_0)\)  for each \(\mathbf {\epsilon }\) , where \(\mathbf {\rho }_0\)  is the canonical pose.
The latent code \(\mathbf {z}\)  and the canonical latent code \(\mathbf {z}_0\)  are mapped to the image \(\mathbf {x}\)  and the canonical image \(\mathbf {x}_0\) .
The identity energy in Eq. (REF ), copied below, encourages the embeddings of the two images to be similar:
\(E_{\text{ID}}(\mathbf {x}_0, \mathbf {x}) = 1 - \cos \big \langle R(\mathbf {x}_0), R(\mathbf {x})\big \rangle , \quad \mathbf {x}_0 = G(\mathbf {z}_0), \mathbf {x}= G(\mathbf {z}).\) 
